Spatial and Temporal Sampling of Polar Regions from Two-Satellite System on Molniya Orbit

VOLUME 28 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY AUGUST 2011

ALEXANDER P. TRISHCHENKO* Network Strategy and Design, Meteorological Service of Canada, Environment Canada, Ottawa, Ontario, Canada

LOUIS GARAND Data Assimilation and Satellite Meteorology Research, Science and Technology Branch, Environment Canada, Dorval, Quebec, Canada

(Manuscript received 22 October 2010, in ﬁnal form 28 January 2011)

ABSTRACT

There has been a signiﬁcant increase of interest in the building of a comprehensive Arctic observing system in recent years to properly and timely track the environmental and climate processes in this vast region. In this regard, a satellite observing system on highly elliptical orbit (HEO) with 12-h period (Molniya type) is of particular interest, because it enables continuous coverage of the entire Arctic region (588–908N) from a constellation of two satellites. Canada is currently proposing to operate such a constellation by 2017. Extending the pioneering study of S. Q. Kidder and T. H. Vonder Haar, this paper presents in-depth analysis of spatiotemporal sampling properties of the imagery from this system. This paper also discusses challenges and advantages of this orbit for various applications that require high temporal resolution and angular sampling.

1. Introduction Increased attention to the Arctic weather is also paid because of significant concerns related to a changing cli- Product latency and refresh rate are among key crit- mate, as this region is broadly anticipated to be the most ical features of a satellite observing system. The ability affected by increasing temperature (Solomon et al. 2007). to acquire and deliver imagery of the earth over large The enhanced melting of sea ice allows significant eco- areas with high temporal resolution is getting increasingly nomic opportunities related to transportation and natural important for weather monitoring, allowing more reliable resources exploration. Deriving high-quality climate re- nowcasting and longer-term forecasts to ensure the safety cords from satellites also requires good temporal sam- of marine, ground, and air transportation. This is espe- pling, especially for rapidly evolving variables such as cially true for the harsh and rapidly changing Arctic en- cloud and radiation. vironment, where climate conditions often put at risk the The current paradigm of satellite meteorology relies survivability of humans in critical situations. The high on the combination of geostationary (GEO) and low temporal frequency of the imagery is very beneficial to earth orbiting (LEO) satellites. The LEO satellites be- track various dangerous environmental conditions that long in most cases to the category of polar orbiters. are common at high latitude such as polar lows, fog, air- Because of synchronous motion of the GEO satellites craft icing, sea ice movements, and volcanic ash transport. with the earth’s rotation, they are perceived as station- ary platforms located over a given nadir position on the equator. The GEO satellites permit continuous obser- * Current affiliation: Canada Centre for Remote Sensing, Ottawa, Canada. vation of the weather within their area of coverage. The constellation of several GEO satellites is currently operating around the earth at any time, which allows Corresponding author address: Alexander P. Trishchenko, Canada Centre for Remote Sensing, 588 Booth Street, Ottawa ON K1A0Y7, continuous coverage of tropical and midlatitude regions Canada. of the earth up to approximately 608. The GEO con- E-mail: [email protected] stellation has been operating as part of the international

DOI: 10.1175/JTECH-D-10-05013.1

977 978 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 28

World Weather Watch Program since 1979. However, by a sufficient number of VIS and IR channels, and to good-quality observations between 608 and 908 latitude carry a suit of detectors for space weather observations zones in the Northern or Southern Hemispheres cannot (PCW 2010). The Russian Federation proposes the be obtained from GEO systems because of oblique view multifunctional space system ‘‘Arktika,’’ which will geometry. High-latitude observations are currently pro- consist of several spacecrafts, including those on HEO vided by LEO satellites. These satellites have a typical orbit. orbital period of about 100 min, and the swath is nor- The advantages of the Molniya orbit for the provision mally below 2500 km. Consequently, there is currently of communication services and some other purposes no source of continuous imagery for the southern or over high-latitude regions have been clearly demon- northern polar regions obtained with sufficiently high strated. Despite this significant success, that orbit has refresh rate. The spatial discontinuity and lack of ade- not been exploited so far for operational meteorological quate temporal sampling significantly affects many ap- applications. This is due to three major factors: com- plications, especially those related to atmospheric motion plexity of the observational geometry created by the vector retrievals; radiation budget; surface parameters; constantly changing satellite altitude and speed, de- estimation of bidirectional reflectance distribution func- manding pointing accuracy for imager and spacecraft, tion (BRDF); and studies linked to cloud life cycle, no- and risk associated with the harsh radiation environment. tably frontal passages. The first two factors, variable altitude and pointing, As demonstrated by Kidder and Vonder Haar (1990), combined with the need for precise image registration, it turns out that continuous coverage of the polar areas impose very strict requirements on the imager scanning can be achieved from satellites launched on a highly system and satellite attitude knowledge and control. The elliptical orbit (HEO). The HEO term covers a number ionizing radiation on Molniya HEO orbit, unlike LEO of potential orbits. A well-established HEO is the and GEO configuration, includes a significant portion of Molniya (‘‘lightning’’ in Russian) orbit used intensively trapped protons that affect spacecrafts twice per orbit by the Soviet Union and the Russian Federation for when passing through the Van Allen radiation belts. communication purposes since 1965. This orbit has Recent feasibility studies conducted for HEO missions a 63.48 inclination, and the orbital period is close to half have concluded that with currently available technology a sidereal day. The spacecraft has a 24-h repeatable it is possible to build a HEO system providing imagery for ground track with two apogees located 1808 apart. The meteorological applications (WMO 2010). In this paper, concept of using high inclination orbits to improve earth we report some new results obtained during preliminary observations over polar latitudes was recently endorsed phases of the PCW system development in Canada. One by the World Meteorological Organization (WMO) major conclusion derived from this effort is that a two- in its ‘‘Vision for the Global Observing System (GOS) satellite system on Molniya orbit is capable of providing in 2025’’ adopted by the 61st session of the WMO Ex- observations with viewing zenith angle (VZA) , 708 ecutive Council (EC-LXI) (WMO 2009). The WMO (recognized limit for quantitative retrievals) continuously document recommends operational implementation of (100% coverage) in the latitude zone between 588 and 908 visible (VIS) and infrared (IR) HEO imagers to monitor and nearly continuous observations in the latitude zone high-latitude phenomena related to winds, clouds, vol- between 458 and 588 with coverage greater than 72% canic ash plumes, sea ice, snow cover, vegetation prop- (;85% on average). The area of continuous coverage erties, and wild fires with sufficient temporal resolution goes down to 388 if VZA , 908. (WMO 2009). The paper is organized as follows: Section 2 provides To address the need in the HEO meteorological a summary of equations and features of Molniya HEO. observing system, the Focus Group for Highly Ellip- Section 3 presents results on the HEO capabilities re- tical Orbits was established as a part of the WMO In- lated to temporal sampling. Section 4 discusses the se- ternational Geostationary Laboratory (IGEOLAB) lection of apogee points and the choice of single orbital initiative. In the framework of IGEOLAB HEO focus plane versus two planes for the constellation. The HEO group, two countries, Canada and the Russian Federa- constellation provides unique capabilities in terms of tion, have announced their plans for HEO missions in viewing geometry for the study of cloud and surface bi- the time frame 2013–16 (WMO 2010). Canada proposes directional reflectance characteristics. This is presented in the Polar Communication and Weather (PCW) satellite section 5. Section 6 concludes the article. Material in system that will consist of a pair of HEO satellites. Each appendix A illustrates orbit layout and provides defini- PCW satellite will be equipped to provide communication of orbital parameters. Appendix B discusses the tion services over the selected high-latitude region, to potential problem of the imaging instrument exposure to carry a multispectral meteorological imager characterized direct sun during observations from Molniya orbit. AUGUST 2011 T R I S H C H E N K O A N D G A R A N D 979

2. Basic properties of Molniya orbit of the oblateness of the earth, its gravitational ﬁeld U(r) is not spherically symmetric. It can be described by This section brieﬂy summarizes the basic equations a harmonic expansion (see, e.g., Duboshin 1976), and properties of HEO Molniya orbit. Mostly because

2 3 ‘ ‘ k k k GM4 rE r0 5 U(r) 5 1 2 å Jk Pk(sinu)1 å å Pkj (sinu)(Ckj cosjl 1 Skj sinjl) , (1) r k52 r k52 r j51

where major semiaxis, and i is the inclination of the orbit . The expressions for higher terms and periodic perturbations r is the radius vector from the center of the earth; can be found in the above references. r, f, and l are the distance (jrj), geocentric latitude, The direct consequence of Eq. (2) is the precession of and longitude, respectively; the orbital plane for all orbits with inclination i 6¼ 908.A G is a gravitational constant; consequence of Eq. (3) is a precession of the perigee r 5 6 378 136.6 m is the earth’s equatorial radius; E within the orbital plane if (5 cos2i 2 1) 6¼ 0. Therefore, if M is the earth’s mass, such that GM 5 3.986 004 3 the following condition holds, 1014 m3 s22;

Jk are zonal harmonics; 2 Ckj, Skj are spherical harmonics; (5 cos i 2 1) 5 0, (5) Pk are Legendre polynomials; and P are the Legendre’s associated functions of degree kj the orbit will be free from secular precession of the k and order j. 2 perigee. This happens when cos i 5 1/5 (i.e., for the The major term that describes the departure of U(r) orbits with critical inclination icr 5 63.4358,whichis ~ from a sphere is deﬁned by the second zonal harmonic the case of Molniya orbit, or symmetrically if icr 5 23 with amplitude J2 5 1.082 635 9 3 10 , which is ap- 116:5658. The argument of perigee for critical orbit proximately three orders of magnitude higher than the should be equal to 2708 to ensure that apogee occurs at other components. An important consequence of the the highest latitude. second zonal harmonic is the existence of secular terms A consequence of Eqs. (2)–(4) is the change in the in the dynamics of Keplerian orbital elements V, v, and satellite mean angular motion n with respect to an in- M, where V is the right ascension of the ascending node ertial frame. This can be expressed as (RAAN), v is the argument of perigee, and M is the mean anomaly. The graphic layout of the elliptical orbit n 5 n 1 M_ , (6) and deﬁnition of orbital elements are described in ap- s pendix A (see Fig. A1). The resulting rates of change

(derivatives) due to contribution from J2 can be ex- where n is a perturbed value of mean angular motion. pressed as follows (see, e.g., El’yasberg 1965; Escobal In order for the satellite ground track to be repeat- 1965; Duboshin 1976): able, the satellite movement around the earth should be precisely synchronized with the earth’s rotation, the 2 precession of the perigee, and the precession of the or- _ 3 rE cosi V 52 J n , (2) bital plane. This occurs when the following condition is s 2 2 a (1 2 e2)2 satisfied (Kidder and Vonder Haar 1990): 3 r 25 cos2i 2 1 v_ 5 J n E , and (3) s 2 2 2 _ _ 4 a (1 2 e ) n 1 v_ s 5 k(Ve 2 Vs), (7) 3 r 23 cos2i 2 1 M_ 5 J n E s 2 3/2 , (4) where k is the number of orbits per sidereal day (e.g., 4 a (1 2 e2) _ k 5 2 for the Molniya orbit) and Ve is rate of the earth’s rotation in an inertial frame, equal to 7.292 115 146 7 3 s n 5 1025 rad s21. Because v_ 5 0 for Molniya orbit, Eq. (7) pwhereffiffiffiffiffiffiffiffiffi index designates secular contributions, s GM/a3/2 is the unperturbed mean motion, a is the reduces to the form 980 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 28

TABLE 1. Some parameters of HEO orbit with inclination icr 5 63.4358 as a function of perigee height Hp.

Decrease in orbital

Perigee height Semimajor axis Apogee height Eccentricity Period period due to J2 RAAN rate ECT period _ 21 Hp (km) a (km) Ha (km) eT(min) DT (s) V (8 yr ) (days) 500 26 553.370 39 850.467 0.740 969 717.738 17.8 254.3 317 600 26 553.567 39 750.860 0.737 205 717.745 17.3 253.0 318 700 26 553.756 39 651.238 0.733 441 717.752 16.9 251.7 319 800 26 553.937 39 551.601 0.729 677 717.759 16.5 250.5 320 900 26 554.112 39 451.950 0.725 913 717.765 16.1 249.4 321 1000 26 554.279 39 352.286 0.722 149 717.771 15.8 248.2 322 1500 26 555.028 38 853.784 0.703 328 717.799 14.1 243.3 326 2000 26 555.653 38 355.033 0.684 506 717.821 12.8 239.1 329

" # pffiffiffiffiffiffiffiffiffi GM 3 r 2 3 cos2i 2 1 500–700 km. Values in Table 1 are provided for the 1 1 J E cr range of perigee height H from 500 to 2000 km. With a3/2 4 2 a (1 2 e2)3/2 p " # increasing Hp, the eccentricity of Molniya orbit de- pffiffiffiffiffiffiffiffiffi 3 GM r 2 cosi creases, the apogee height decreases, and the orbital 5 2 V_ 1 J E cr . (8) e 2 3/2 2 period slightly increases (,5 s). The most noticeable 2 a a (1 2 e2) effect occurs for the rate of change of the ascending node 21 Equation (8) can be solved for the semimajor axis a,if (RAAN), which reduces from about 548 to 398 yr as the eccentricity e is fixed. It can be done by selecting the perigee height increases from 500 to 2000 km. A direct consequence of the ECT drift is that solar illu- perigee height Hp above the earth, which is defined as mination conditions at the apogee point change from

a(1 2 e) 5 rE 1 Hp. (9) local solar noon to midnight in the course of ;5.3 months. It is still true that the imagery acquired from Some parameters computed from the above equations HEO observing system is subjected to the entire possi- as a function of perigee height Hp are listed in Table 1 ble range of the solar zenith angles (SZA) at all locations for the Molniya orbit with inclination icr 5 63.4358. From within the polar region during the course of one day Eqs. (2)–(4), the orbital period for the Molniya orbit because of continuous observations. However, obser- with perigee in the range of 500–700 km should be ap- vations at any given location are obtained at different proximately 17–18 s shorter than half of a sidereal day relative azimuth angle (RAA); that is, the diurnal cycle for the ground track to be repeatable. This also leads to of the relationship between SZA and RAA is continu- the precession of the orbit by 528–548 yr21 in the nega- ously evolving from day to day. More details are pro- tive direction for the ascending node V. This precession vided below in section 5. ~ accelerates the rate of change for beta angle (the angle If the inclination icr 5 116:5658 is selected, then the between the direction to the sun and the orbital plane) rate of change of the ascending node deﬁned by Eq. (2) that happens due to the motion of the earth around the has a different sign. This has an impact on the solution of sun. As such, the local solar equator crossing time (ECT) Eq. (8). Corresponding results are provided in Table 2. in the ascending node is continuously changing so that it One can see that this choice of inclination leads to an makes a compete 24-h cycle (3608 rotation) approxi- increase of the semimajor axis and an increase of orbital mately in 317–319 days for a perigee height in the range period relative to the previous case with icr 5 63.4358.

~ TABLE 2. Some parameters of HEO orbit with inclination icr 5 116:5658 as a function of perigee height Hp. Increase in orbital

Perigee height Semimajor axis Apogee height Eccentricity Period period due to J2 RAAN rate ECT period _ 21 Hp (km) a (km) Ha (km) eT(min) DT (s) V (8 yr ) (days) 500 26 567.963 39 879.654 0.741 112 718.330 17.8 54.3 430 600 26 567.807 39 779.340 0.737 346 718.322 17.3 53.0 428 700 26 567.656 39 679.039 0.733 581 718.316 16.9 51.7 426 800 26 567.512 39 578.751 0.729 815 718.309 16.5 50.5 425 900 26 567.374 39 478.474 0.726 050 718.303 16.1 49.3 423 1000 26 567.241 39 378.209 0.722 284 718.297 15.8 48.2 421 1500 26 566.649 38 877.026 0.703 458 718.270 14.1 43.2 415 2000 26 566.159 38 376.046 0.684 631 718.247 12.8 39.1 409 AUGUST 2011 T R I S H C H E N K O A N D G A R A N D 981

This occurs because the precession of the ascending node has a different sign than the rotation of the earth. The satellite has to return later to the same spot at the equator to compensate for this difference in plane precession. The major consequence is a slight increase in the apogee altitude by ;(21–29) km and an increase in the ECT period by 80–113 days, depending on perigee height. For example, for a perigee height at 500 km, the apogee height increases from 39 850.467 to 39 879.654 km and ECT increases from 317 to 430 days. Comparing orbits with two values of critical inclination, preference is given to the case of Molniya orbit with icr 5 63.4358 on the basis of better viewing conditions at the apogee because of smaller ground speed and launch requirements, which are easier for this choice of orbit inclination. For the re- mainder of this paper, the orbit with inclination icr 5 63.4358 is considered. The typical orbital geometry configuration for one FIG. 1. A 3D view of the Molniya orbit. Molniya satellite is shown in Fig. 1 in 3D projection. The satellite moves very fast and is close to the earth’s surface in the perigee region in the Southern Hemisphere. from apogee. This scale factor indicates the impact of When the satellite reaches the apogee location, its the altitude variation on the imagery pixel size, which is movement is synchronized with the earth’s rotation such a unique feature of HEO orbits. This factor varies from that it spends a very significant amount of time over 1.06 at the apogee point to 1.04, 0.96, 0.84, and 0.64 at 1, a limited geographical region, thus providing a ‘‘quasi 2, 3, and 4 h from the apogee point. In other words, the geostationary’’ viewpoint. pixel size varies from 16% to 216% relative to a ref- The nominal working imaging interval is defined by erence altitude within normal imaging period 63 h, and the period 63 h around the apogee time. Between 3 and it reduces by up to 36% during the extended imaging 4 h from the apogee, a reduced but still good coverage of period (3–4 h from apogee). Figure 2b shows the vari- the polar region can be achieved, and that period of ation of the latitude of the subsatellite point as a func- imaging is in fact needed to maximize coverage of the tion of longitude. Within 64 h, the longitude range is circumpolar domain. This extended period adds 2 h per less than 638, whereas the latitude changes by almost orbit and 4 h day21 of imaging from each satellite. From 168. The subsatellite point is located above 558N during a two-satellite system, the combination of nominal im- the 63-h interval around the apogee. The minimum aging and extended imaging allows obtaining dual views latitude at 4 h from apogee is greater than 468. Figure 2 of the region and therefore additional opportunities for depicts the variation of ground speed. It is less than retrievals of geophysical parameters between 2 and 4 h 50 m s21 within 1 h, less than 100 m s21 within 2 h, less from the apogee (i.e., during 8 h day21). Best stereo than 200 m s21 within 3 h, and less than 350 m s21 within views are obtained 3 h from apogee because the two 4 h. Assuming that the image scan duration is less than satellites would be nearly at the same height. For cre- 30 s, the subsatellite point moves on the earth’s surface ating composite images, the ideal demarcation is the less than 6 km during nominal imaging and less than point where the viewing zenith angle is the same for both 10.5 km during extended imaging time. Assuming in ad- satellites. dition that the scanning over 2D detector array in the Plots of the dynamics for several parameters of the focal plane takes less than 1 s, the band-to-band pixel Molniya orbit over a 64-h interval around the apogee displacement due to satellite motion varies with the al- are shown in Fig. 2. Plots correspond to the orbit with titude of the satellite by less than 50, 100, 200, and 350 m perigee height of 500 km. Figure 2a shows the variation for points at 1, 2, 3, and 4 h from apogee. Figure 2d of altitude versus time. It changes from 39 850 km at shows the effect of VZA on pixel size during the working apogee to approximately 39 000, 36 200, 31 500, and part of the orbit. Although there is some dependence 24 000 km at 1, 2, 3, and 4 h from the apogee point. of this effect on altitude, it can be assumed that the Figure 2a also depicts the ratio of the altitude at a par- change of pixel size with VZA is altitude independent for ticular point of the orbit to that at a reference altitude Molniya orbit, as seen in Fig. 2d. For comparison, Fig. 2d selected equal to 37 500 km, representative of 1.5 h also shows the VZA dependence for a typical LEO orbit 982 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 28

FIG. 2. Variation of the Molniya orbit parameters over the imaging interval. Perigee height is 500 km. (a) Altitude and altitude scale factor vs time, (b) latitude vs longitude with regard to apogee point, (c) ground speed of the subsatellite point, and (d) pixel growth factor vs VZA.

with 800-km altitude. The pixel growth factor is com- against electrons, although the total ionizing radiation puted as a ratio of pixel size at particular VZA to that at dose may not be significantly different from that experi- nadir (VZA 5 08). The pixel size increases by a factor of enced on a GEO orbit according to calculations based on 1.5 at 458, 2.0 at 578, and 3.0 at 688 for the altitude range the European Space Agency (ESA) Space Environment within the working part of the Molniya orbit. The VZA Information System (SPENVIS) (http://www.spenvis.oma. effect on pixel size is therefore larger than that created by be/). This issue along with consideration of alternate HEO the changing altitude. orbits requires an in-depth evaluation, which is beyond An important consideration for the Molniya orbit is the scope of this paper. the radiation environment. Unlike LEO and GEO sat- Another important question is related to the stability ellites, the spacecraft on Molniya orbit crosses the Van of the Molniya orbit. The analysis described by Eqs. (2)– Allen radiation belts, consisting of trapped protons, (8) accounts for the first-order perturbations from zonal twice per orbit. This circumstance presents a specific harmonic with amplitude J2. It can be shown that the challenge for electronics, detectors, and other equipment, libration (or long-term oscillation) effect for the argu- because shielding against protons is more difficult than ment of perigee v exists around a critical inclination AUGUST 2011 T R I S H C H E N K O A N D G A R A N D 983

FIG. 3. The long-term variations of orbital parameters for the Molniya-2/9 spacecraft (NORAD ID 07276). Launch date: 26 Apr 1974. (a) Period, (b) argument of perigee, (c) perigee height above the earth’s surface, (d) inclination, (e) RAAN, and (f) mean anomaly.

value when higher orders for J2 are included (Jupp oscillations in the argument of perigee (Fig. 3b), incli- 1988). Effects from higher-order harmonics of the earth’s nation (Fig. 3d), perigee height (Fig. 3c), and mean gravitational field and atmospheric drag also play a role. anomaly (Fig. 3f) can be observed. The precession of the The lunisolar effects cause important long-term pertur- ascending node is nearly linear and is described by Eq. bations for the Molniya orbit (Delhaise and Morbidelli (2) with good accuracy. It can be seen that, in late 1989– 1993; Jupp 1988). In particular, they can cause a signifi- early 1990, the perigee height reduced to very low values cant impact on the eccentricity of the Molniya orbit. below 150 km. During the first half of 1990, the satellite This, in turn, can decrease the height of perigee to low transitioned to an orbit with a period around 640.6 min values, where the atmospheric drag has very significant from an initial ‘‘critical’’ value of about 717.8 min. The impact on the orbital dynamics and can even lead to a results presented in Fig. 3 demonstrate that Molniya orbit premature decay of the satellite (Delhaise and Morbidelli can be generally stable, but parameters could oscillate 1993). An example of the multidecadal time series of around critical values and perturbation effects some- orbital parameters for spacecraft Molniya-2/9 [the North times could be very strong. Therefore, the orbit should American Aerospace Defense Command (NORAD) be properly controlled to ensure a repeatable ground identification (ID) 07276] is shown in Fig. 3. The period track with fixed apogee locations and to prevent pre- spans a time interval of more than 35 yr. The long-term mature decay. 984 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 28

FIG. 4. Temporal coverage of the northern latitudes from Molniya orbit expressed as percentage of time. Observations are conducted within 64 h around the apogee. One- and two- satellite systems are considered for maximum VZA equal to (left) 708 and (right) 908.

3. Temporal coverage close to those of apogee locations (Fig. 4a). With VZA extended to 908, the entire distribution moves southward One of the key performance characteristics of HEO by about 208. The shape of geographic distribution of observing system is its ability to provide continuous temporal coverage from the two-satellite system in two imagery over the high-latitude regions. To maintain orbital planes is similar to the one-satellite system. It is continuous coverage over the polar regions, the two explained by the fact that in both cases the satellites satellites on 12-h HEO orbit should obviously be 6-h follow the same ground track, and the working part apart; that is, when one satellite reaches the apogee, the of the orbit, where the imaging is conducted, is limited second one should be at the perigee point. If the satel- to a relatively small region, as depicted in Fig. 2b. The lites are launched in two orbital planes with their RAAN geographical distribution of temporal coverage is in separated by 908 and proper temporal synchronization this case highly uneven along the longitude direction between apogee and perigee, as explained above, they will follow the same ground track, resulting in only two apogee points. In contrast, the conﬁguration in a single orbital plane results in 4 apogee points separated in longitude by 908. Figure 4 depicts the temporal coverage of the high- latitude regions from one-satellite and two-satellite systems with spacecrafts placed in one orbital plane or two orbital planes. Left panels correspond to maximum VZA equal to 708, and right panels correspond to VZAmax 5 908. All calculations are conducted assuming satellite operations within a 64-h period around the apogee point; that is, the satellite altitude is greater than 24 000 km and can reach almost 40 000 km (Fig. 2a). Results are expressed as a proportion of the total observed time per day as a percentage. The one-satellite system provides a highly uneven geographic distribution of temporal coverage along the longitude direction (Figs. 4a,d). The maximum temporal coverage reaches approximately FIG. 5. As in Fig. 4, but for zonal-mean temporal coverage. Two- 67%. For the case VZA , 708, it can be as low as 35% in satellite systems in one orbital plane and two orbital planes have the zone between 408 and 558 latitude at the longitudes similar coverage and are shown by the same curve. AUGUST 2011 T R I S H C H E N K O A N D G A R A N D 985

FIG. 6. The map of minimum VZA observed for two-satellite system in (a) one orbital plane and (b) two orbital planes.

(Figs. 4c,f), although it reaches 100% at certain locations, because satellites replace each other over the apogee points. For example, for condition of VZA , 708, 100% coverage is achieved at latitudes slightly below 658 and can go down to latitudes around 408 for longitudes between the apogee points (Fig. 4c). For condition VZA , 908 and two-satellite system in two orbital planes, the distribution (Fig. 4f) is shifted in the southward direction by 208. FIG. 7. Satellite ground tracks for two-satellite system on Molniya The coverage pertaining to the two-satellite system in orbit in one orbital plane selected for the PCW project: (a) global one orbital plane is much more uniform along the lon- map and (b) polar view. The solid line corresponds to satellite 1, and gitude direction (Figs. 4b,e). The 100% line follows the dashed line corresponds to satellite 2. approximately 588 parallel for VZA , 708 and 388 for VZA , 908. The area between 508 and 588 is more than 80% covered for VZA , 708. The zonal-mean temporal calculated assuming satellite operations within a 64-h coverage is presented in Fig. 5. Figure 5 shows results for period around the apogee point. the one- and two-satellite systems with VZA , 708 and Figure 6 depicts the map of a minimum VZA observed VZA , 908. Because results are very close for the two- at a particular location in the Northern Hemisphere. satellite system in one and two orbital planes, they are not Figure 6a shows results for two-satellite system in one shown separately. The two-satellite system provides con- orbital plane. Figure 6b shows results for two-satellite tinuous temporal coverage (100%) with VZA , 708 above system in two orbital planes. Minimum VZA is an im- 588 latitude, .94% above 558 latitude, .80% above 508 portant consideration to determine the best viewing con- latitude, .72% above 458 latitude, and .55% above ditions for a number of applications when close to nadir 308 latitude. Again, the distribution moves southward observations are preferable, such as surface parameter by 208 for VZA , 908. Results shown in Fig. 5 are mapping, for example. Again, the two-satellite system in 986 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 28

FIG. 8. The sequence of earth views from the Molniya orbit within 64-h period around the apogee.

one orbital plane provides more uniform geographical when spatial resolution matters. The higher spatial distribution and reduces the average VZA over the area resolution is important for land application and for at- of interest. mospheric motion vector retrievals. To observe North Following previous analysis, the scenario with one America landmass at smaller VZA, one apogee should orbital plane is seen as preferable in comparison to the be centrally located over the continent. The longitude two-orbital-planes scenario. This scenario also appears 958W serves a good central line for this purpose. Once strategically more favorable from the point of view of initial apogee is selected; the remaining apogees are a spare satellite. The spare satellite can be placed in the deﬁned automatically at 58W, 858E, and 1758E. Apogees same orbital plane and equally distanced between two should occur one after the other in clockwise fashion operational spacecrafts: that is, with 3-h time difference (next apogee 908 to the west of current one). This con- or 908 shift in the mean anomaly. The drifting of a spare ﬁguration is shown in Fig. 7. The top panel displays satellite into any of two working position represents an latitude–longitude projection. The bottom panel dis- easier maneuver than changing the RANN for the sce- plays polar view. The temporal sequence of the earth nario of two orbital planes. views at 24, 23, 0, 13, and 14 h is displayed in Fig. 8. ‘‘Blue marble’’ composites created from the Moderate Resolution Imaging Spectroradiometer (MODIS) at 4. Apogee selection and dual view capability the National Aeronautics and Space Administration Following the decision to retain the one-plane con- (NASA) Goddard Space Flight Center were used as stellation as a baseline scenario, the next step is to select input imagery for simulations (http://visibleearth.nasa. the location of the four apogee points. Selection criteria gov/). The circle marks the 508N parallel. The angular were based on viewing conditions over landmasses. size of the earth disk is approximately 24.28 at 4 h from Because of angular dependence of pixel size (see Fig. the apogee, is 19.48 at 3 h, and is equal to 15.88 at the 2d), it is preferable to have observations close to nadir apogee point. AUGUST 2011 T R I S H C H E N K O A N D G A R A N D 987

FIG. 9. Temporal coverage of dual views from two-satellite system on Molniya orbit expressed as percentage of time. Observations are conducted within 64 h around the apogee. Two-satellite systems in (left) one and (right) two orbital planes are considered for maximum VZA equal to 708 and 908.

As indicated earlier, the two-satellite system presents conﬁguration, the angular difference between directions an interesting opportunity for dual-view observations. is on average smaller, because both satellites are located In the period 2–4 h from the apogee point, both sat- within a relatively small region around the same apogee ellites can image polar regions simultaneously from (Fig. 2b). In the case of one orbital plane, dual views are two different directions. The geographic distribution of temporal coverage with dual views is presented in Fig. 9. The results for one-orbital-plane scenario are shown on the left, and those for the two-orbital-planes scenario are shown on the right. Two cases of VZA conditions are considered. The top panels present results for the case VZA , 708, and the bottom panels present results when VZA , 908. Again, one-orbital-plane conﬁguration has more uniform geographic distribution. For the case of one orbital plane and VZA , 708, dual views are possible more than 30% of the time above 678 latitude. Dual views are available for 20% of time above 608 latitude. The zonal-mean temporal coverage of dual views from the two-satellite system in one orbital plane and two orbital planes are shown in Fig. 10. For the case of VZA , 908, the distribution shifts southward by approximately 208. The geographic distribution of dual-view conditions for the two-orbital-planes scenario is highly uneven in the longitude direction. Although the areal coverage of FIG. 10. As in Fig. 9, but for zonal-mean temporal coverage of dual dual views is slightly larger for the two-orbital-planes views from Molniya system. 988 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 28

FIG. 11. The distribution of VZA vs SZA at (608N, 458W) for different solar local time at the apogee point: summer solstice (23 Jun). always obtained from two different regions separated by satellite orbital plane relative to direction to the sun, 908 in longitude, as shown in Figs. 7a,b. which is caused by a combined effect of the earth’s motion around the sun and precession of the orbital plane described by Eq. (2) and is also shown in Fig. 3e. 5. Dynamics of solar and viewing conditions from As in the GEO case, the observations from Molniya Molniya orbit orbit also cover the entire range of solar illumination As discussed in previous sections, the observing ge- conditions for every point in the area of interest during ometry from Molniya orbit differs significantly from that a 24-h period. However, it occurs at different VZA, characterizing LEO and GEO satellites. The opera- because the spacecraft moves as sketched in Fig. 2b, with tional meteorological observations from LEO orbits changes in altitude as indicated in Fig. 2a. The obser- are mostly conducted from sun-synchronous satellites vations are also conducted from four separate locations by imagers operating in cross-track scanning mode. As corresponding to the four apogee positions (Fig. 7). such, the solar zenith angle is a strict function of latitude Another factor that defines the sun–satellite geometry is and season. The distribution of VZA versus RAA is also local solar time at apogee point. This time varies from quite limited (see Luo et al. 2008). The SZA for the day to day and makes a complete 24-h cycle as described imagery from GEO platform takes all possible values in Tables 1 and 2 by the ECT period. For the perigee at during the course of the day, but the VZA value is fixed 500 km, this period is equal to 317 days for inclination ~ for a particular point. icr 5 63.4358 and 430 days for icr 5 116:5658. In general, there are three cycles of the solar illumi- Some examples of the distributions are presented in nation conditions for the imaging from Molniya orbit: 1) Figs. 11 and 12 for the point located at (608N, 458W) and diurnal cycle caused by the earth’s rotation; 2) seasonal in Figs. 13 and 14 for the point located at (608N, 908W). cycle caused by movement of the earth around the sun These figures show four panels that correspond to dif- and the tilting of the earth’s axis; and 3) rotation of the ferent local solar time at apogee point, as determined by AUGUST 2011 T R I S H C H E N K O A N D G A R A N D 989

FIG. 12. The distribution of VZA vs RAZ at (608N, 458W) for different solar local time at the apogee point: summer solstice (23 Jun).

the universal time (UTC) when the satellite reaches the possible. All possible distributions of SZA, VZA, and 958W apogee position. Four times are considered: 00, 06, RAA cannot be shown here; nevertheless, Figs. 11–14 12, and 18 UTC. The date of summer solstice is selected provide evidence of the rich angular sampling available (22 June). The baseline two-satellite system in one or- from Molniya orbit. The wide range of VZA and RAA bital plane is assumed. The choice of UT values and date combined with the full range of SZA and the dual view uniquely defines the angle between the satellite orbital capability are very beneficial for a variety of applications. plane and the sun. These include retrievals of albedo, surface bidirectional From Fig. 11, it can be seen that during the course of reflectance function, radiation budgets, cloud properties, one day the observations at all solar zenith angles are atmospheric motion vectors, surface temperature, aero- conducted. The values of SZA . 908 are also shown, cor- sol, and many other parameters. responding to nighttime conditions. Because the point is located at 458W, the VZA is always greater than 208, 6. Conclusions which means that this point cannot be observed at nadir. Observations made from each apogee region can be This paper extends the study of Kidder and Vonder clearly identified. The VZA range is wide, and the dis- Haar (1990). A detailed analysis of orbital properties tribution varies depending on the angle between the and spatiotemporal sampling of polar regions from orbital plane and the sun. Molniya orbit is presented. Two-satellite systems in one Figure 12 displays the distribution of VZA versus or two orbital planes with RAAN separated by 908 were RAA in a polar diagram. VZA is plotted as polar radius analyzed. It was found that the two-satellite system in and RAA is plotted as polar angle. The distribution one orbital plane provides better and more uniform appears quite complex. The wide range of RAA is geographical coverage of observations and dual views covered with values observed close to the principal over the northern latitudes. It is therefore recommended (RAA 5 08 or 1808) and perpendicular planes (RAA 5 that satellites should be launched in one orbital plane. 908 or 2708). Figures 13 and 14 are similar to Figs. 11 and The recommended locations of apogees are 958W, 58W, 12, except that they correspond to a pixel location at 858E, 1758E, which ensures coverage of landmasses with (608N, 908W), a point where VZA values near zero are better views at smaller viewing zenith angles. 990 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 28

FIG. 13. As in Fig. 11, but at (608N, 908W).

It has been shown that the two-satellite system on represent a breakthrough by providing unique observa- Molniya orbit can provide seamless observations above tion capabilities at high latitudes. That system would also 588N with viewing zenith angles not exceeding 708.Con- be beneficial for communications and space weather tinuous observations with viewing zenith angles less than applications. The HEO concept was recently endorsed 908 can be obtained for a much larger area extending by the World Meteorological Organization (WMO), be- down to 388N. cause it would represent a major contribution to the The two-satellite Molniya system provides very rich earth’s observing system. For the first time, the global observational geometry that includes the entire diurnal satellite observing system will have a capability to con- cycle of the solar zenith angle, as well as a wide range of tinuously observe weather at any point and any time, thus viewing zenith angles and relative azimuth angles over fulfilling the meteorologist’s dream existing for many any particular location in the area of interest. The ob- generations. servations along the principal plane (RAA 5 08–1808) and perpendicular plane (RAA 5 908–2708) are normally Acknowledgments. Authors gratefully acknowledge obtained on a daily basis. This feature is very beneficial the use of the North American Aerospace Defense for various applications requiring good angular sampling, Command (NORAD) Two Line Element (TLE) data- such as bidirectional reflectance, radiation budget, and base maintained by Dr. T.S. Kelso (http://celestrak.com/ cloud retrievals. The two-satellite system also provides NORAD/elements/). The ‘‘blue marble’’ composites very unique capability of dual views that is available created from the Moderate Resolution Imaging Spec- 20%–33% of the time above 608N. This feature has troradiometer (MODIS) by Reto Sto¨ ckli at the NASA special value to assign heights for estimated atmospheric Goddard Space Flight Center (http://visibleearth.nasa. motion vectors. gov/) were used as an input imagery for simulations of The implementation of a meteorological satellite earth views from Molniya orbit. We thank our colleague system on Molniya or other types of HEO orbit would Dr. Josep Aparicio for a careful review of the manuscript. AUGUST 2011 T R I S H C H E N K O A N D G A R A N D 991

FIG. 14. As in Fig. 12, but at (608N, 908W).

APPENDIX A shape and position of the orbit, such as a, e, v, V, i, and different true anomaly n angles to ensure that, when one Definition of Orbital Elements satellite is at apogee, the second satellite is in perigee (i.e., 6 h apart). For orbital configuration discussed above The graphic layout for definition of orbital elements is in the text, when two satellites are moving in two orbital presented in Fig. A1, which corresponds to the inertial planes, they have RAAN angles that differ by 908. Their coordinate system (Duboshin 1976; Escobal 1965). Point true anomaly n angles also differ to ensure that passages O denotes the center of the earth. The z axis is directed of perigee and apogee points are properly synchronized. to the north along the earth’s spin axis. The x axis is Because of the earth’s rotation, the 6-h period leads to the directed to the vernal equinox point. The perigee point same ground track for both satellites in the two-orbital- corresponds to the closet point to the earth’s center, and planes configuration discussed above. the apogee point corresponds to the farthest point. The distance from the earth’s center to the perigee point is equal to a(1 2 e) and the distance from the earth’s center to the apogee point is equal to a(1 1 e), where a is the semimajor axis and e is the eccentricity of the orbit. The argument of perigee v is the angle between direction to perigee and direction from the earth’s center to the ascending node. The angle between direction to the ascending node and x axis is called the right ascension of the ascending node (RAAN) and denoted as V. Position of the satellite on the orbit is determined by the angle n, which is called the true anomaly. The angle i between orbital plane and equatorial plane is called the orbit inclination. For orbital configuration discussed above with two

Molniya satellites moving in the same orbital plane, both FIG. A1. Graphic layout for elliptical orbit and deﬁnition of Keplerian satellites have identical orbital elements related to the orbital elements. 992 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 28

Although, a 5 10.58 is a relatively large angle, pre- caution measures may still be needed to ensure that no signiﬁcant stray light illumination occurs because of the position of the sun close to the instrument ﬁeld of view. The instrument should be switched into the safe mode and properly protected from the direct sun illumination that may occur outside of imaging hours.

REFERENCES

Delhaise, F., and A. Morbidelli, 1993: Luni-solar effects of geo- FIG. B1. Geometry for minimum sun angle over the earth disk for synchronous orbits at the critical inclination. Celestial Mech. Molniya orbit. Dyn. Astron., 57, 155–173. Duboshin, G. N., 1976: Spravochnoe Rukovodstvo po Nebesnoi APPENDIX B Mekhanike I Astrodynamike (The Reference Manual on Celestial Mechanics and Astrodynamics). 2nd ed. Nauka, 864 pp. El’yasberg, P. E., 1965: Introduction to the Theory of Flight of Artiﬁcial Potential Instrument Exposure to Direct Sun Earth Satellites. Nauka, NASA TT F-391, TT 67-51399, 357 pp. Escobal, P. R., 1965: Methods of Orbit Determination. John Wiley Because of the potentially damaging consequence of and Sons, 463 pp. direct sun on the satellite imaging system, it is of interest Jupp, H. A., 1988: The critical inclination problem—30 years of to determine if direct illumination by the sun ever occurs progress. Celestial Mech., 43, 127–138. during the imaging operations from Molniya orbit: that Kidder, S. Q., and T. H. Vonder Haar, 1990: On the use of satellites in Molniya orbits for meteorological observation of middle is, 64 h around the apogee. This takes place twice a day and high latitudes. J. Atmos. Oceanic Technol., 7, 517–522. for GEO satellites, during sunset and sunrise intervals, Luo, Y., A. P. Trishchenko, and K. V. Khlopenkov, 2008: De- when the sun approaches the edge of the earth’s disk. veloping clear-sky, cloud and cloud shadow mask for pro- Figure B1 depicts geometrical conditions for the mini- ducing clear-sky composites at 250-meter spatial resolution for mum sun angle to the earth’s disk observed from Molniya the seven MODIS land bands over Canada and North America. Remote Sens. Environ., 112, 4167–4185. orbit. This occurs around the winter solstice and when PCW, 2010: Polar Communication and Weather mission: User the relative azimuth angle equals 1808 for the satellite requirement document. Version 5.1, 111 pp. located at latitude f 5 468N when it starts (or com- Solomon, S., D. Qin, M. Manning, M. Marquis, K. Averyt, M. M. B. pletes) the imaging operations at 4 h from apogee Tignor, H. L. Miller Jr., and Z. Chen, Eds., 2007: Climate (Fig. 2b). The angle b is approximately 12.18. The earth’s Change 2007: The Physical Science Basis. Cambridge Uni- versity Press, 996 pp. tilt angle is d 5 23.48. Therefore, the minimum elevation WMO, 2009: WMO vision for the GOS in 2025. Proc. Ninth Con- angle a 5 f 2 b 2 d 5 10.58. Thus, during the imaging of sultative Meeting on High-Level Policy on Satellite Matters, the earth’s disk within 64 h around the apogee, the Port of Spain, Trinidad and Tobago, WMO, 19 pp. [Available smallest angular distance that the sun comes close to the online at http://www.wmo.int/pages/prog/sat/meetings/documents/ earth’s disk is greater than 108. Outside of this time in- cm9_Doc_08_GOSVision2025.pdf.] ——, 2010: The International Geostationary Laboratory (IGeoLab) terval (and therefore for the range of satellite altitudes for highly elliptical orbit focus group. WMO Final Rep., below 24 000 km), the sun may approach the edge of the 9 pp. [Available online at http://www.wmo.int/pages/prog/ earth’s disk. Figure B1 presents the worst case scenario. sat/documents/igeolabheo3FinalReport.pdf.]